%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:35:18 PM UTC 2026
% Result : Unsatisfiable 8.81s 1.57s
% Output : CNFRefutation 8.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 81 ( 81 unt; 0 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 118 ( 118 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : product(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : product(A,difference(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : difference(A,product(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] : quotient(product(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : product(quotient(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] : difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : i(A) = difference(A,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : j(A) = quotient(one,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : product(i(A),A) = product(A,j(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : eta(A) = product(i(A),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] : product(i(i(A)),B) = product(eta(A),product(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B] : product(A,product(eta(A),B)) = product(j(j(A)),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] : product(eta(A),product(B,C)) = product(product(eta(A),B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B,C] : l(A,B,C) = difference(product(A,B),product(A,product(B,C))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0] : product(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0,X1] : product(X0,difference(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f25,plain,
! [X0,X1] : difference(X0,product(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0,X1] : quotient(product(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
! [X0,X1] : product(quotient(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] : difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0] : i(X0) = difference(X0,one),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
! [X0] : j(X0) = quotient(one,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
! [X0] : product(i(X0),X0) = product(X0,j(X0)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f33,plain,
! [X0] : eta(X0) = product(i(X0),X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f34,plain,
! [X0,X1] : product(i(i(X0)),X1) = product(eta(X0),product(X0,X1)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f35,plain,
! [X0,X1] : product(X0,product(eta(X0),X1)) = product(j(j(X0)),X1),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f37,plain,
! [X0,X1,X2] : product(eta(X0),product(X1,X2)) = product(product(eta(X0),X1),X2),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f38,plain,
! [X0,X1,X2] : l(X0,X1,X2) = difference(product(X0,X1),product(X0,product(X1,X2))),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f42,plain,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f52,plain,
! [X0] : eta(X0) = product(X0,j(X0)),
inference(forward_demodulation,[status(thm)],[f32,f33]) ).
fof(f60,plain,
! [X0] : product(X0,eta(X0)) = product(j(j(X0)),one),
inference(paramodulation,[status(thm)],[f22,f35]) ).
fof(f62,plain,
! [X0] : product(X0,eta(X0)) = j(j(X0)),
inference(forward_demodulation,[status(thm)],[f22,f60]) ).
fof(f87,plain,
! [X0] : product(j(X0),X0) = one,
inference(paramodulation,[status(thm)],[f31,f27]) ).
fof(f163,plain,
! [X0] : product(X0,i(X0)) = one,
inference(paramodulation,[status(thm)],[f30,f24]) ).
fof(f207,plain,
! [X0] : quotient(one,i(X0)) = X0,
inference(paramodulation,[status(thm)],[f163,f26]) ).
fof(f208,plain,
! [X0,X1] : quotient(X0,difference(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f209,plain,
! [X0] : quotient(j(j(X0)),eta(X0)) = X0,
inference(paramodulation,[status(thm)],[f62,f26]) ).
fof(f211,plain,
! [X0,X1] : quotient(product(j(j(X0)),X1),product(eta(X0),X1)) = X0,
inference(paramodulation,[status(thm)],[f35,f26]) ).
fof(f214,plain,
! [X0] : j(i(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f31,f207]) ).
fof(f241,plain,
! [X0] : difference(j(X0),one) = X0,
inference(paramodulation,[status(thm)],[f87,f25]) ).
fof(f253,plain,
! [X0] : i(j(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f30,f241]) ).
fof(f281,plain,
! [X0] : eta(i(X0)) = product(i(X0),X0),
inference(paramodulation,[status(thm)],[f214,f52]) ).
fof(f287,plain,
! [X0] : quotient(eta(X0),j(X0)) = X0,
inference(paramodulation,[status(thm)],[f52,f26]) ).
fof(f309,plain,
! [X0] : quotient(j(X0),eta(i(X0))) = i(X0),
inference(paramodulation,[status(thm)],[f214,f209]) ).
fof(f411,plain,
! [X0,X1,X2] : product(difference(X0,product(product(X0,X1),X2)),X0) = product(X1,product(X2,X0)),
inference(paramodulation,[status(thm)],[f28,f27]) ).
fof(f447,plain,
! [X0] : product(i(i(X0)),i(X0)) = product(eta(X0),one),
inference(paramodulation,[status(thm)],[f163,f34]) ).
fof(f449,plain,
! [X0] : product(i(i(X0)),eta(X0)) = product(eta(X0),j(j(X0))),
inference(paramodulation,[status(thm)],[f62,f34]) ).
fof(f482,plain,
! [X0] : eta(i(i(X0))) = product(eta(X0),one),
inference(forward_demodulation,[status(thm)],[f281,f447]) ).
fof(f483,plain,
! [X0] : eta(i(i(X0))) = eta(X0),
inference(forward_demodulation,[status(thm)],[f22,f482]) ).
fof(f581,plain,
! [X0] : quotient(X0,eta(i(i(X0)))) = i(i(X0)),
inference(paramodulation,[status(thm)],[f214,f309]) ).
fof(f587,plain,
! [X0] : quotient(X0,eta(X0)) = i(i(X0)),
inference(forward_demodulation,[status(thm)],[f483,f581]) ).
fof(f602,plain,
! [X0] : product(i(i(X0)),eta(X0)) = X0,
inference(paramodulation,[status(thm)],[f587,f27]) ).
fof(f613,plain,
! [X0] : product(eta(X0),j(j(X0))) = X0,
inference(forward_demodulation,[status(thm)],[f449,f602]) ).
fof(f658,plain,
! [X0] : quotient(one,product(eta(X0),j(X0))) = X0,
inference(paramodulation,[status(thm)],[f87,f211]) ).
fof(f681,plain,
! [X0] : j(product(eta(X0),j(X0))) = X0,
inference(forward_demodulation,[status(thm)],[f31,f658]) ).
fof(f715,plain,
! [X0] : quotient(X0,j(j(X0))) = eta(X0),
inference(paramodulation,[status(thm)],[f613,f26]) ).
fof(f763,plain,
! [X0] : quotient(product(eta(X0),j(X0)),j(X0)) = eta(product(eta(X0),j(X0))),
inference(paramodulation,[status(thm)],[f681,f715]) ).
fof(f770,plain,
! [X0] : quotient(eta(product(eta(X0),j(X0))),X0) = product(eta(X0),j(X0)),
inference(paramodulation,[status(thm)],[f681,f287]) ).
fof(f772,plain,
! [X0] : i(X0) = product(eta(X0),j(X0)),
inference(paramodulation,[status(thm)],[f681,f253]) ).
fof(f783,plain,
! [X0] : eta(X0) = eta(product(eta(X0),j(X0))),
inference(forward_demodulation,[status(thm)],[f26,f763]) ).
fof(f795,plain,
! [X0] : quotient(eta(X0),X0) = product(eta(X0),j(X0)),
inference(forward_demodulation,[status(thm)],[f783,f770]) ).
fof(f802,plain,
! [X0] : i(X0) = quotient(eta(X0),X0),
inference(forward_demodulation,[status(thm)],[f795,f772]) ).
fof(f885,plain,
! [X0] : product(i(X0),X0) = eta(X0),
inference(paramodulation,[status(thm)],[f802,f27]) ).
fof(f1356,plain,
! [X0,X1,X2] : difference(product(eta(X0),X1),product(eta(X0),product(X1,X2))) = X2,
inference(paramodulation,[status(thm)],[f37,f25]) ).
fof(f1371,plain,
! [X0,X1,X2] : l(eta(X0),X1,X2) = X2,
inference(forward_demodulation,[status(thm)],[f38,f1356]) ).
fof(f1425,plain,
! [X0,X1] : l(X0,j(X1),X1) = difference(product(X0,j(X1)),product(X0,one)),
inference(paramodulation,[status(thm)],[f87,f38]) ).
fof(f1475,plain,
! [X0,X1] : l(X0,j(X1),X1) = difference(product(X0,j(X1)),X0),
inference(forward_demodulation,[status(thm)],[f22,f1425]) ).
fof(f8207,plain,
! [X0,X1] : X0 = difference(product(eta(X1),j(X0)),eta(X1)),
inference(paramodulation,[status(thm)],[f1371,f1475]) ).
fof(f8354,plain,
! [X0,X1] : quotient(eta(X0),X1) = product(eta(X0),j(X1)),
inference(paramodulation,[status(thm)],[f8207,f208]) ).
fof(f8525,plain,
! [X0,X1] : product(X0,quotient(eta(X0),X1)) = product(j(j(X0)),j(X1)),
inference(paramodulation,[status(thm)],[f8354,f35]) ).
fof(f8583,plain,
product(x0,quotient(eta(x0),product(x1,x0))) != j(x1),
inference(backward_demodulation,[status(thm)],[f8525,f42]) ).
fof(f9249,plain,
! [X0,X1] : product(difference(X0,one),X0) = product(X1,product(i(product(X0,X1)),X0)),
inference(paramodulation,[status(thm)],[f163,f411]) ).
fof(f9361,plain,
! [X0,X1] : product(i(X0),X0) = product(X1,product(i(product(X0,X1)),X0)),
inference(forward_demodulation,[status(thm)],[f30,f9249]) ).
fof(f9363,plain,
! [X0,X1] : eta(X0) = product(X1,product(i(product(X0,X1)),X0)),
inference(forward_demodulation,[status(thm)],[f885,f9361]) ).
fof(f12485,plain,
! [X0,X1] : eta(X0) = product(difference(X0,X1),product(i(X1),X0)),
inference(paramodulation,[status(thm)],[f24,f9363]) ).
fof(f13304,plain,
! [X0,X1] : eta(X0) = product(difference(X0,j(X1)),product(X1,X0)),
inference(paramodulation,[status(thm)],[f253,f12485]) ).
fof(f16781,plain,
! [X0,X1] : quotient(eta(X0),product(X1,X0)) = difference(X0,j(X1)),
inference(paramodulation,[status(thm)],[f13304,f26]) ).
fof(f16926,plain,
product(x0,difference(x0,j(x1))) != j(x1),
inference(backward_demodulation,[status(thm)],[f16781,f8583]) ).
fof(f16929,plain,
j(x1) != j(x1),
inference(forward_demodulation,[status(thm)],[f24,f16926]) ).
fof(f16930,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f16929]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:40:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 8.81/1.57 % Refutation found
% 8.81/1.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.81/1.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.66/1.63 % Elapsed time: 1.256670 seconds
% 3.66/1.63 % CPU time: 9.792020 seconds
% 3.66/1.63 % Total memory used: 250.793 MB
% 3.66/1.63 % Net memory used: 243.180 MB
%------------------------------------------------------------------------------